WORKING PAPERS

Xu, Y.*, Tan, K. S., Pan, G, and Zhu, W. (2021). Sustainable Area-Yield Insurance Program with Optimal Risk Pooling: A Behavior-Based Machine Learning Approach. [SSRN], [PDF].

Area-yield insurance is a promising alternative to address challenges that hinder the sustainability of traditional individual-loss insurance programs, including moral hazard, high administration costs, and data sparsity. However, the efficiency of areayield insurance contracts is often diminished due to the presence of basis risk. In this paper, we propose a behavior-based machine learning approach to optimally determine risk pools, leading to a more sustainable area-yield insurance program. We begin by selecting the optimal number of risk pools, analyzing producers’ farming behavior under area-yield insurance contracts through a utility maximization framework. Then, we employ an unsupervised spectral clustering model to group producers into these risk pools. This machine learning technique pools producers with similar production histories together, enhancing the efficiency of the area-yield insurance contract and addressing challenges of high-dimensionality and computational complexity. Our proposed optimal risk pooling procedure is empirically tested and cross-compared with data from major corn production counties in the U.S. heartland region. The empirical results show that our method significantly reduces contract basis risk and mitigates producers’ tail risk. Furthermore, compared to alternative statistical methods, our framework produces risk pooling results that are more effective in risk reduction, offering both geographical and economic insights. 

Keywords:  Sustainability, Area yield, Basis risk, Crop insurance, Machine learning.

Xu, Y.*, Tan, K. S., and Zhu, W. (2022). A Geo-Hierarchical Deep Learning Approach for Flood Insurance Modeling and Pricing. [SSRN], [PDF] (Previously titled "Borrowing Information Across Space and Time: Pricing Flood Risk with Physics-based Hierarchical Machine Learning Models")

Flood risk is an increasingly urgent concern as climate change intensifies the frequency and severity of extreme events. Flood insurance is a key tool to protect against such risk, but its modeling and pricing remain challenging. This paper proposes a Geo-Hierarchical Deep Learning (GHDL) framework, a scalable, interpretable, and cost-efficient approach, to generate high-resolution flood hazard factors and inform insurance pricing. The GHDL framework can effectively capture spatial dependencies that are essential for an accurate flood risk assessment by incorporating geographical connectivity directly into deep learning models. Using data from the Mississippi River Basin, we show that GHDL achieves 86%–91% accuracy in extreme scenarios, outperforming climate-uninformed and benchmark deep learning models. Applied to the National Flood Insurance Program (NFIP), GHDL-derived hazard factors reduce net premiums by 33.5% and solvency capital requirements by 32.3%. These improvements enhance pricing adequacy and contribute to the long-term sustainability of public flood insurance programs.

Keywords:  Flood risk, Climate risk, Deep learning, Ratemaking, Colvency capital requirement.

Feng, Q., Jaidee, S.**, Pan, G., and Zhu, W. (2022). Robust Testing in High-Dimensional Linear Model, Working Paper. 

We propose a joint significance of many coefficients in high-dimensional linear regression that is robust to unconditional heteroskedasticity and autocorrelation of unknown form within regression errors. Exploiting information on the limiting behaviors of an equally weighted empirical spectral distribution with its weighted counterpart, we derive the asymptotic property of proposed statistics without a priori knowledge of the sparsity level of tested parameters and the underlying structure of regression errors. Instead, we adopt the Random Matrix Theory and self-normalization technique to comprehend the curse of dimensionality, heteroskedasticity, and autocorrelation simultaneously. Thanks to the naturality of parametric framework, the limiting Gaussian distribution of our proposed statistics are free from the choice of kernel functions and bandwidth selections. Simulation studies confirm the accuracy of type-I error with satisfactory empirical testing power in a finite sample over many different types of dependent data such as time-series data and spatially dependent data. In practice, to avoid an upward size distortion from using conventional statistics, we recommend practitioners take the curse of dimensionality into account when the intensity ratio is greater than 0.05.